[ 1 ] check whether -3 and 3 are the zeroes of the polynomial x² - 9.
1 answer:
Answer:
<h3>#1</h3>- x² - 9 = 0
- x² = 9
- x = ± √9
- x = ± 3
Yes, -3 and 3 are zeroes of this polynomial
<h3>#2</h3><em>See attached graphs</em>
Zero's of a polynomial are the intersection of the graph with the x-axis.
They include coordinates as (x, 0), so the x-coordinates are zero's.
The attached shows the zero's.
<h3>#3</h3><em>See attached graphs</em>
Zero's of each polynomial are reflected in the graphs.
- () y = x² - x - 6 has zeros x = -2 and x = 3
- (ii) y = 6 - x - x² has zero's x = -3, x = 2
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The slope-point formula:
We have:
Substitute:
Answer:
a) 20.16; b) 20.49 and 21.51
Step-by-step explanation:
We use z scores for each of these. The formula for a z score is
.
For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.
Using this, 21 as the mean and 1 as the standard deviation,
-0.84 = (X-21)/1
-0.84 = X-21
Add 21 to each side:
-0.84+21 = X-21+21
20.16 = X
For part b, we want the middle 39%. This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want
50-19.5 = 30.5% = 0.305 and
50+19.5 = 69.5% = 0.695.
Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:
-0.51 = (X-21)/1
-0.51 = X-21
Add 21 to each side:
-0.51+21 = X-21+21
20.49 = X
0.51 = (X-21)/1
0.51 = X-21
Add 21 to each side:
0.51+21 = X-21+21
21.51 = X